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Popular >

derivative of arctan(1/(3x))

Solution

\frac{d}{d x} (arctan (\frac{1}{3 x}))

Solution

- \frac{3}{1 + 9 x ^{2}}

Solution steps

\frac{d}{d x} (arctan (\frac{1}{3 x}))

Apply the chain rule:

\frac{1}{( \frac{1}{3 x} ) ^{2} + 1} \frac{d}{d x} (\frac{1}{3 x})

= \frac{1}{( \frac{1}{3 x} ) ^{2} + 1} \frac{d}{d x} (\frac{1}{3 x})

\frac{d}{d x} (\frac{1}{3 x}) = - \frac{1}{3 x ^{2}}

= \frac{1}{( \frac{1}{3 x} ) ^{2} + 1} (- \frac{1}{3 x ^{2}})

Simplify

\frac{1}{( \frac{1}{3 x} ) ^{2} + 1} (- \frac{1}{3 x ^{2}}) : - \frac{3}{1 + 9 x ^{2}}

= - \frac{3}{1 + 9 x ^{2}}

Popular Examples

sum from n=0 to infinity of 3(1/2)^n

n = 0 \sum \infty 3 (\frac{1}{2})^{n}

d/(d{r)}(({r})/(sqrt({r)^2+5)})

\frac{d}{d r} (\frac{r}{r ^{2} + 5})

(\partial)/(\partial y)(x^2+y)

\frac{\partial}{\partial y} (x^{2} + y)

tangent of f(x)=(3x+1)/(x^2+1),(1,2)tangent of

f (x) = \frac{3 x + 1}{x ^{2} + 1}, (1, 2)

limit as t approaches 3 of (2t-3)/(t-3)

t \to 3 lim (\frac{2 t - 3}{t - 3})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(1/(3x)) ?
The derivative of arctan(1/(3x)) is -3/(1+9x^2)
What is the first derivative of arctan(1/(3x)) ?
The first derivative of arctan(1/(3x)) is -3/(1+9x^2)